It was only a few months ago that Nicole was living in the Dimansion with EJ. So I have no problem believing that Sydney remembers her. Sydney has excellent taste...

I don't know why, but I completely forgot about that. You're right, it is conceivable.

I guess it just seems out of the blue now, since we haven't seen Sydney and Nicole have any scenes since.

It is very out of the blue. You'd think the son she just lost would be the only child on her mind and she'd be doing something in his memory like lighting a candle at St Luke's. But if we get another spoiler concerning Nicole and Sydney, I'd say they're going somewhere with it.

Chad and Nicole have a discussion about Sydney the week before, and Chad offers to buy Sydney a gift from Nicole. The video call in Jason's script thread is either from EJ letting Sydney thank Nicole (although if Chad is buying the gift, how would EJ/Syd know it's from Nicole?) or it's from Chad to let Nicole see Syd enjoying her gift.